We present an evolution equation governed by a maximal monotone operator with exponential rate of convergence to a zero of the maximal monotone operator. When the maximal monotone operator is the subdifferential of a convex, proper, and lower semicontinuous function, we show that the trajectory of...
the graph of alinear function 是一条直线line,这条直线的函数表达式也称作直线方程Equations of a straight line,斜截式gradient-intercept form是y=ka+b,其中常数k称为这条直线的斜率gradient,b称为这条直线的y截距y-intercept。 我们需要知道的是: x截距x-intercept是方程中y=0时得到的x值,也叫做函数的零点...
This important principle, evidently discovered independently by three groups, was important in that the shape of the gradient (in this case a simple exponential) was employed to optimize the behavior of particle zones. Later Noll (1967) formalized the tactic with a whole family of gradient shapes...
In this section we propose the gbex algorithm to estimate the GPD parameters (σ(x),γ(x)) using gradient boosting to build an ensemble of tree predictors. The algorithm is the standard Friedman’s boosting algorithm Friedman (2001, 2002) applied with objective function given by the GPD nega...
Production optimization, also known as well control optimization, focuses on assigning values to the control settings of wells (bottom-hole pressure (BHP) or flow rate) over a pre-defined or adaptive control intervals. The aim is to optimize an objective function over the reservoir lifespan. The...
The noise variance was estimated from four ROIs, consisting of 300 voxels, at the corners of the noise-only background. When the bipolar readouts were used, amplitude modulation was also modelled as an exponential function and corrected for experimental datasets22. The spin density and T2* ...
as “noise”; as such, they require some formof robust outlier rejection in fitting the vignetting function. They also require segmentation and must explicitly account for local shading. All these are susceptible to errors. We are also interested in vignetting correction using a ...
G can subsequently be optimized by optimize(G) so that the exponential is computed only once, to obtain proc(x, y) local df, t; t := exp(-x); df := array(1 .. 1); df[1] := y + 1; return -df[1]*t, t end proc One can obtain derivatives of any function ...
In this paper, using results of [5], we prove an exponential convergence rate of Law(θn) to μλ under Assumption 2.1. More importantly, a functional central limit theorem is established under the additional Assumption 2.2. In the sequel, ϕ:Rd→R denotes an at most polynomially growing...
A simple choice for a direction of search to find a minimum is to take d(k) as the negative gradient vector at the point x(k). For a sufficiently small step value this can be shown to guarantee a reduction in the function value. This leads to an algorithm of the form (1.5)x(k+...